A genetic model involving body colour and eye colour of fruit flies predicts that offspring will consist of four phenotypes in the ratio \(9 : 3 : 3 : 1\).
A random sample of 200 such offspring is taken. Their phenotypes are found to be as follows.
Phenotype
Brown body Red eye
Brown body Brown eye
Black body Red eye
Black body Brown eye
Frequency
125
37
32
6
Relative proportion from model
9
3
3
1
Carry out a test, using a \(2.5 \%\) level of significance, of the goodness of fit of the genetic model to these data.
The median length of European fruit flies is 2.5 mm . South American fruit flies are believed to be larger than European fruit flies. A random sample of 12 South American fruit flies is taken. The flies are found to have the following lengths (in mm).
\(1.7 \quad 1.4\)
\(3.1 \quad 3.5\)
3.8
4.2
2.2
2.9
4.4
2.6
\(3.9 \quad 3.2\)
Carry out a Wilcoxon signed rank test, using a \(5 \%\) level of significance, to test this belief.